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In this lesson, we will learn how to find the matrix of the linear transformation represented by the differential operator.

Q1:

Consider the vector space of polynomials of degree three at most. The differentiation operator π· is a linear transformation on this vector space. Find the matrix that represents the linear transformation πΏ = π· + 5 π· + 4 2 with respect to the basis ο© 1 , π₯ , π₯ , π₯ ο΅ 2 3 .

Q2:

Apply the linear differential operator π· to evaluate the following expression: οΉ π· β 2 π· + 4 ο οΉ π₯ π + 5 π₯ + 2 ο 2 π₯ 2 .

Q3:

Consider the vector space of infinitely differentiable functions. The differentiation operator π· is a linear transformation on this vector space. Find the general form of an element of the kernel of the linear transformation π΄ = π· + 2 π· + 1 2 .

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